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300
ANALYTICAL MECHAJNJLUs
= a cos (a>£ + 5') « a cos w (i + fo')
233.  Common Forms of Equation (III). — The following are the typical forms in which equation (III) is written ; x = a sin (tat + S) = a sin co (t + 4)
(mo
where 6' = ~ - 5 and V - T - *o-2                      4
234.   Epoch. — The constants i0 and C are called epochs, and 5 and 5' are called epoch angles.   The meanings of these constants will be seen from Fig. 131,
235.   Velocity. — The following expressions for the velocity of the particle maybe obtained either from equation (II) or from equation (III) :
v =
V^-
V«X
(I)   Is the displacement - time curve
(II)  is the velocity - time curv©
FIG, 132.
It is evident from these expressions that the velocity is ; simple harmonic function of the time, that it has the sam